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A Parameterized Algorithm for Packing Overlapping Subgraphs

  • Jazmń Romero
  • Alejandro López-Ortiz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8476)

Abstract

Finding subgraphs with arbitrary overlap was introduced as the k-H-Packing with t-Overlap problem in [10]. Specifically, does a given graph G have at least k induced subgraphs each isomorphic to a graph H such that any pair of subgraphs share at most t vertices? This problem has applications in the discovering of overlapping communities in real networks. In this work, we introduce the first parameterized algorithm for the k-H-Packing with t-Overlap problem when H is an arbitrary graph of size r. Our algorithm combines a bounded search tree with a greedy localization technique and runs in time O(r rk k (r − t − 1)k + 2 n r ), where n = |V(G)|, r = |V(H)|, and t < r. Applying similar ideas we also obtain an algorithm for packing sets with possible overlap which is a version of the k-Set Packing problem.

Keywords

Greedy Algorithm Search Tree Parameterized Algorithm Maximal Solution Feasible Path 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Adamcsek, B., Palla, G., Farkas, I., Derenyi, I., Vicsek, T.: Cfinder: locating cliques and overlapping modules in biological networks. Bioinformatics 22(8), 1021–1023 (2006)CrossRefGoogle Scholar
  2. 2.
    Damaschke, P.: Fixed-parameter tractable generalizations of cluster editing. In: The 6th International Conference on Algorithms and Complexity (CIAC), pp. 344–355 (January 2006)Google Scholar
  3. 3.
    Fellows, M., Guo, J., Komusiewicz, C., Niedermeier, R., Uhlmann, J.: Graph-based data clustering with overlaps. Discrete Optimization 8(1), 2–17 (2011)CrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    Fellows, M., Heggernes, P., Rosamond, F., Sloper, C., Telle, J.: Finding k disjoint triangles in an arbitrary graph. In: The 30th Workshop on Graph-Theoretic Concepts in Computer Science (WG), pp. 235–244 (2004)Google Scholar
  5. 5.
    Fellows, M., Knauer, C., Nishimura, N., Ragde, P., Rosamond, F., Stege, U., Thilikos, D., Whitesides, S.: Faster fixed-parameter tractable algorithms for matching and packing problems. Algorithmica 52(2), 167–176 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    Hartung, S., Komusiewicz, C., Nichterlein, A.: On structural parameterizations for the 2-club problem. In: van Emde Boas, P., Groen, F.C.A., Italiano, G.F., Nawrocki, J., Sack, H. (eds.) SOFSEM 2013. LNCS, vol. 7741, pp. 233–243. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  7. 7.
    Komusiewicz, C., Sorge, M.: Finding dense subgraphs of sparse graphs. In: 7th International Symposium on Parameterized and Exact Computation (IPEC), pp. 242–251 (2012)Google Scholar
  8. 8.
    Moser, H.: A problem kernelization for graph packing. In: Nielsen, M., Kučera, A., Miltersen, P.B., Palamidessi, C., Tůma, P., Valencia, F. (eds.) SOFSEM 2009. LNCS, vol. 5404, pp. 401–412. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  9. 9.
    Prieto, E., Sloper, C.: Looking at the stars. Theoretical Computer Science 351(3), 437–445 (2006)CrossRefzbMATHMathSciNetGoogle Scholar
  10. 10.
    Romero, J., López-Ortiz, A.: The \({\mathcal{G}}\)-packing with t-overlap problem. In: Pal, S.P., Sadakane, K. (eds.) WALCOM 2014. LNCS, vol. 8344, pp. 114–124. Springer, Heidelberg (2014)CrossRefGoogle Scholar
  11. 11.
    Schäfer, A., Komusiewicz, C., Moser, H., Niedermeier, R.: Parameterized computational complexity of finding small-diameter subgraphs. Optimization Letters 6(5), 883–891 (2012)CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Jazmń Romero
    • 1
  • Alejandro López-Ortiz
    • 1
  1. 1.David R. Cheriton School of Computer ScienceUniversity of WaterlooCanada

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